A novel fractal interpolation function algorithm for fractal dimension estimation and coastline geometry reconstruction: a case study of the coastline of Kingdom of Saudi Arabia

• Published in: The European physical journal. B, Condensed matter physics Vol. 97; no. 4; p. 51
• Main Authors: Husain, Akhlaq, Gumma, Suhas, Sajid, Mohammad, Reddy, Jaideep, Alresheedi, Mohammad T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024; Springer; Springer Nature B.V
• Subjects: Algorithms; Case studies; Coasts; Complex Systems; Condensed Matter Physics; Dividers; Dynamic programming; Estimation; Flow charts; Fluid- and Aerodynamics; Fractal geometry; Fractals; Geometry; Interpolation; Methods; Multiprocessing; Numerical analysis; Physics; Physics and Astronomy; Python; Recent Advances in Complex Systems; Regular Article - Statistical and Nonlinear Physics; Search algorithms; Simulation; Solid State Physics; Saudi Arabia
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/s10051-024-00696-2

Fractal dimension represents the geometric irregularity of an object with respect to the underlying space and is used for several characterizations. The divider method and the box counting method are two classical methods to compute the fractal dimension of fractals, coastlines, natural objects and other complex systems. In this work, we present a novel, extremely efficient algorithm based on the fractal interpolation function (FIF) method for estimating the fractal dimension of coastlines and for reconstructing the coastline geometry. The algorithm is implemented for the coastline of the Kingdom of Saudi Arabia (KSA) as a case study. For validating the accuracy of the proposed algorithm in estimating the fractal dimension we compare our results with those obtained using the divider and the box-counting method. We also reconstruct the coastline geometry of KSA using our algorithm which generates functions (interpolants) that matches the coastline geometry very accurately. Numerical simulations are obtained using a robust, parallel multi-processing library, an R - program, Python codes, a dynamic programming algorithm, binary search algorithm and the QGIS software. Graphical abstract KSA coastline geometry, methodology and flowchart of the proposed FIF algorithm